1.
$$\mathbf { M } = \left( \begin{array} { l l }
4 & - 5
2 & - 7
\end{array} \right)$$
- Show that the matrix \(\mathbf { M }\) is non-singular.
The transformation \(T\) of the plane is represented by the matrix \(\mathbf { M }\).
The triangle \(R\) is transformed to the triangle \(S\) by the transformation \(T\).
Given that the area of \(S\) is 63 square units, - find the area of \(R\).
- Show that the line \(y = 2 x\) is invariant under the transformation \(T\).